A music company wants to design a cardboard box for mailing a 22-CD set measuring 14.2 cm by 12.4 cm by 2.5 cm. what amount of suface area will the box have? ​

At first students may find the sum of all the areas of the faces.

$$ \begin{alignat}{3} \text{Front: } (5)(9.5) &=47.5 \text{ in}^2 &\qquad \text{Top: } (5)(30) &= 150 \text{ in}^2 &\qquad \text{Right side: } (9.5)(30) &= 285 \text{ in}^2 \\ \text{Back: } (5)(9.5) &=47.5 \text{ in}^2 &\qquad \text{Bottom: } (5)(30) &= 150 \text{ in}^2 &\qquad \text{Left side: } (9.5)(30) &= 285 \text{ in}^2 \end{alignat} $$

Sum of the areas of the 6 faces: $SA = 47.5 + 47.5 + 150+ 150 + 285 + 285 = 965 \text{ in}^2$

Using the surface area formula:

$$ \begin{align} SA &= 2wl + 2lh + 2wh \\ SA &= 2(5)(30) + 2(30)(9.5) + 2(5)(9.5) \\ SA &= 965 \text{ in}^2 \end{align} $$

Students may continue to use the sum of all the areas of the faces to find the surface area which gives the same value as using the surface area formula which is shown below.

Setup of boxDimensions

2 cylinders wide by 1 cylinder high by 3 cylinders long10 in. wide by 9.5 in. high by 15 in. long

$$ \begin{align} SA &= 2wl + 2lh + 2wh \\ SA &= 2(10)(15) + 2(15)(9.5) + 2(10)(9.5) \\ SA &= 775 \text{ in}^2 \end{align} $$